My layman's interpretation of the language would be as follows:

1) "A procedure turn is the maneuver prescribed *when it is necessary
to
perform a course reversal*..."

2) [When it is necessary to perform a course reversal,] "The procedure
turn or hold in lieu of procedure turn is a required maneuver."

3) [Even when it is necessary to perform a course reversal,] "The
procedure turn is not required when the symbol "No PT" is shown, when
RADAR VECTORING to the final approach course is provided, when
conducting a timed approach, or when the procedure turn is not
authorized."

This begs the question, "when is it necessary to perform a course
reversal?" Someone mentioned a descent of 300 feet or a turn of more
than 30 degrees according to TERPS (not according to anything we
studied to get our IFR ticket, as far as I recall), though that doesn't
seem right to me. I think even a 90 degree intercept or 1000 feet (or
more) of descent may be okay if you're far enough from the FAF.